ABSTRACT
In this chapter, we provide a tutorial of modeling and analyzing significant key performance indicators (KPIs) of massive multi-input multi-output (MIMO) systems in a downlink Rayleigh fading channel. Initially, we provide an exposition of deriving closed-form expression of outage probability (OP) of the instantaneous signal-to-interference-plus-noise ratio (SINR) for arbitrary beamforming vectors. The analysis is based on unknown instantaneous channel state information (CSI), however statistical CSI is taken to be known. Knowing the definition of the outage probability, we evaluate it by calculating the probability that the SINR is less than a certain threshold value. This is done by expressing the SINR as the ratio of indefinite quadratic forms (IQF) and utilizing the multi-dimensional complex Gaussian random variable distribution to formulate the required probability in terms of a multi-dimensional integral. This integral is evaluated using the property of the multi-dimensional Gaussian integral, which results in the analytical expression of OP. Next, we propose a constrained optimization problem to obtain optimum beam vectors for all users by minimizing the linearized sum of all the users’ outage probabilities while constraining the beam powers to unity for fairness. Simulation results are presented to support our theoretical findings.
